What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=e^x ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=e^x is y=c_{1}e^x+c_{2}xe^x+(e^xx^2)/2

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(d^2y)/(dx^2)-2(dy)/(dx)+y=e^x

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{2}}{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{2}}{2}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{e ^{x} x ^{2}}{2}

\int \frac{25 - 16 x ^{2}}{x} d x

\frac{\partial}{\partial x} (\frac{y}{y ^{2} + x ^{2}})

\int_{- 1}^{1} x cos (nπ x) d x

\int \frac{1}{1 - v ^{2}} d v

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=e^x ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)+y=e^x is y=c_{1}e^x+c_{2}xe^x+(e^xx^2)/2